Ideas from 'Logical Pluralism' by JC Beall / G Restall [2006], by Theme Structure

[found in 'Logical Pluralism' by Beall,J/Restall,G [OUP 2006,978-0-19-928841-0]].

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3. Truth / A. Truth Problems / 1. Truth
Some truths have true negations
                        Full Idea: Dialetheism is the view that some truths have true negations.
                        From: JC Beall / G Restall (Logical Pluralism [2006], 7.4)
                        A reaction: The important thing to remember is that they are truths. Thus 'Are you feeling happy?' might be answered 'Yes and no'.
3. Truth / B. Truthmakers / 5. What Makes Truths / b. Objects make truths
A truthmaker is an object which entails a sentence
                        Full Idea: The truthmaker thesis is that an object is a truthmaker for a sentence if and only if its existence entails the sentence.
                        From: JC Beall / G Restall (Logical Pluralism [2006], 5.5.3)
                        A reaction: The use of the word 'object' here is even odder than usual, and invites many questions. And the 'only if' seems peculiar, since all sorts of things can make a sentence true. 'There is someone in the house' for example.
4. Formal Logic / E. Nonclassical Logics / 2. Intuitionist Logic
(∀x)(A v B) |- (∀x)A v (∃x)B) is valid in classical logic but invalid intuitionistically
                        Full Idea: The inference of 'distribution' (∀x)(A v B) |- (∀x)A v (∃x)B) is valid in classical logic but invalid intuitionistically. It is straightforward to construct a 'stage' at which the LHS is true but the RHS is not.
                        From: JC Beall / G Restall (Logical Pluralism [2006], 6.1.2)
                        A reaction: This seems to parallel the iterative notion in set theory, that you must construct your hierarchy. All part of the general 'constructivist' approach to things. Is some kind of mad platonism the only alternative?
4. Formal Logic / E. Nonclassical Logics / 5. Relevant Logic
It's 'relevantly' valid if all those situations make it true
                        Full Idea: The argument from P to A is 'relevantly' valid if and only if, for every situation in which each premise in P is true, so is A.
                        From: JC Beall / G Restall (Logical Pluralism [2006], 5.2)
                        A reaction: I like the idea that proper inference should have an element of relevance to it. A falsehood may allow all sorts of things, without actually implying them. 'Situations' sound promising here.
Excluded middle must be true for some situation, not for all situations
                        Full Idea: Relevant logic endorses excluded middle, ..but says instances of the law may fail. Bv¬B is true in every situation that settles the matter of B. It is necessary that there is some such situation.
                        From: JC Beall / G Restall (Logical Pluralism [2006], 5.2)
                        A reaction: See next idea for the unusual view of necessity on which this rests. It seems easier to assert something about all situations than just about 'some' situation.
Relevant logic does not abandon classical logic
                        Full Idea: We have not abandoned classical logic in our acceptance of relevant logic.
                        From: JC Beall / G Restall (Logical Pluralism [2006], 5.4)
                        A reaction: It appears that classical logic is straightforwardly accepted, but there is a difference of opinion over when it is applicable.
Relevant consequence says invalidity is the conclusion not being 'in' the premises
                        Full Idea: Relevant consequence says the conclusion of a relevantly invalid argument is not 'carried in' the premises - it does not follow from the premises.
                        From: JC Beall / G Restall (Logical Pluralism [2006], 5.3.3)
                        A reaction: I find this appealing. It need not invalidate classical logic. It is just a tougher criterion which is introduced when you want to do 'proper' reasoning, instead of just playing games with formal systems.
Relevant logic may reject transitivity
                        Full Idea: Some relevant logics reject transitivity, but we defend the classical view.
                        From: JC Beall / G Restall (Logical Pluralism [2006], 8)
                        A reaction: [they cite Neil Tennant for this view] To reject transitivity (A?B ? B?C ? A?C) certainly seems a long way from classical logic. But in everyday inference Tennant's idea seems good. The first premise may be irrelevant to the final conclusion.
A doesn't imply A - that would be circular
                        Full Idea: We could reject the inference from A to itself (on grounds of circularity).
                        From: JC Beall / G Restall (Logical Pluralism [2006], 8)
                        A reaction: [Martin-Meyer System] 'It's raining today'. 'Are you implying that it is raining today?' 'No, I'm SAYING it's raining today'. Logicians don't seem to understand the word 'implication'. Logic should capture how we reason. Nice proposal.
4. Formal Logic / E. Nonclassical Logics / 6. Free Logic
Free logic terms aren't existential; classical is non-empty, with referring names
                        Full Idea: A logic is 'free' to the degree it refrains from existential import of its singular and general terms. Classical logic must have non-empty domain, and each name must denote in the domain.
                        From: JC Beall / G Restall (Logical Pluralism [2006], 7.1)
                        A reaction: My intuition is that logic should have no ontology at all, so I like the sound of 'free' logic. We can't say 'Pegasus does not exist', and then reason about Pegasus just like any other horse.
5. Theory of Logic / A. Overview of Logic / 1. Overview of Logic
Syllogisms are only logic when they use variables, and not concrete terms
                        Full Idea: According to the Peripatetics (Aristotelians), only syllogistic laws stated in variables belong to logic, and not their applications to concrete terms.
                        From: JC Beall / G Restall (Logical Pluralism [2006], 2.5)
                        A reaction: [from Lukasiewicz] Seems wrong. I take it there are logical relations between concrete things, and the variables are merely used to describe these relations. Variables lack the internal powers to drive logical necessities. Variables lack essence!
Logic studies consequence; logical truths are consequences of everything, or nothing
                        Full Idea: Nowadays we think of the consequence relation itself as the primary subject of logic, and view logical truths as degenerate instances of this relation. Logical truths follow from any set of assumptions, or from no assumptions at all.
                        From: JC Beall / G Restall (Logical Pluralism [2006], 2.2)
                        A reaction: This seems exactly right; the alternative is the study of necessities, but that may not involve logic.
5. Theory of Logic / A. Overview of Logic / 2. History of Logic
The view of logic as knowing a body of truths looks out-of-date
                        Full Idea: Through much of the 20th century the conception of logic was inherited from Frege and Russell, as knowledge of a body of logical truths, as arithmetic or geometry was a knowledge of truths. This is odd, and a historical anomaly.
                        From: JC Beall / G Restall (Logical Pluralism [2006], 2.2)
                        A reaction: Interesting. I have always taken this idea to be false. I presume logic has minimal subject matter and truths, and preferably none at all.
5. Theory of Logic / A. Overview of Logic / 4. Pure Logic
Logic studies arguments, not formal languages; this involves interpretations
                        Full Idea: Logic does not study formal languages for their own sake, which is formal grammar. Logic evaluates arguments, and primarily considers formal languages as interpreted.
                        From: JC Beall / G Restall (Logical Pluralism [2006], 2.1)
                        A reaction: Hodges seems to think logic just studies formal languages. The current idea strikes me as a much more sensible view.
5. Theory of Logic / A. Overview of Logic / 8. Logic of Mathematics
The model theory of classical predicate logic is mathematics
                        Full Idea: The model theory of classical predicate logic is mathematics if anything is.
                        From: JC Beall / G Restall (Logical Pluralism [2006], 4.2.1)
                        A reaction: This is an interesting contrast to the claim of logicism, that mathematics reduces to logic. This idea explains why students of logic are surprised to find themselves involved in mathematics.
5. Theory of Logic / B. Logical Consequence / 2. Types of Consequence
There are several different consequence relations
                        Full Idea: We are pluralists about logical consequence because we take there to be a number of different consequence relations, each reflecting different precisifications of the pre-theoretic notion of deductive logical consequence.
                        From: JC Beall / G Restall (Logical Pluralism [2006], 8)
                        A reaction: I don't see how you avoid the slippery slope that leads to daft logical rules like Prior's 'tonk' (from which you can infer anything you like). I say that nature imposes logical conquence on us - but don't ask me to prove it.
5. Theory of Logic / B. Logical Consequence / 4. Semantic Consequence |=
A sentence follows from others if they always model it
                        Full Idea: The sentence X follows logically from the sentences of the class K if and only if every model of the class K is also a model of the sentence X.
                        From: JC Beall / G Restall (Logical Pluralism [2006], 3.2)
                        A reaction: This why the symbol |= is often referred to as 'models'.
5. Theory of Logic / I. Semantics of Logic / 3. Logical Truth
Logical truth is much more important if mathematics rests on it, as logicism claims
                        Full Idea: If mathematical truth reduces to logical truth then it is important what counts as logically true, …but if logicism is not a going concern, then the body of purely logical truths will be less interesting.
                        From: JC Beall / G Restall (Logical Pluralism [2006], 2.2)
                        A reaction: Logicism would only be one motivation for pursuing logical truths. Maybe my new 'Necessitism' will derive the Peano Axioms from broad necessary truths, rather than from logic.
5. Theory of Logic / L. Paradox / 6. Paradoxes in Language / d. The Preface paradox
Preface Paradox affirms and denies the conjunction of propositions in the book
                        Full Idea: The Paradox of the Preface is an apology, that you are committed to each proposition in the book, but admit that collectively they probably contain a mistake. There is a contradiction, of affirming and denying the conjunction of propositions.
                        From: JC Beall / G Restall (Logical Pluralism [2006], 2.4)
                        A reaction: This seems similar to the Lottery Paradox - its inverse perhaps. Affirm all and then deny one, or deny all and then affirm one?
10. Modality / A. Necessity / 3. Types of Necessity
Relevant necessity is always true for some situation (not all situations)
                        Full Idea: In relevant logic, the necessary truths are not those which are true in every situation; rather, they are those for which it is necessary that there is a situation making them true.
                        From: JC Beall / G Restall (Logical Pluralism [2006], 5.2)
                        A reaction: This seems to rest on the truthmaker view of such things, which I find quite attractive (despite Merricks's assault). Always ask what is making some truth necessary. This leads you to essences.
18. Thought / A. Modes of Thought / 1. Thought
Judgement is always predicating a property of a subject
                        Full Idea: All judgement, for Kant, is essentially the predication of some property to some subject.
                        From: JC Beall / G Restall (Logical Pluralism [2006], 2.5)
                        A reaction: Presumably the denial of a predicate could be a judgement, or the affirmation of ambiguous predicates?
19. Language / C. Assigning Meanings / 8. Possible Worlds Semantics
We can rest truth-conditions on situations, rather than on possible worlds
                        Full Idea: Situation semantics is a variation of the truth-conditional approach, taking the salient unit of analysis not to be the possible world, or some complete consistent index, but rather the more modest 'situation'.
                        From: JC Beall / G Restall (Logical Pluralism [2006], 5.5.4)
                        A reaction: When I read Davidson (and implicitly Frege) this is what I always assumed was meant. The idea that worlds are meant has crept in to give truth conditions for modal statements. Hence situation semantics must cover modality.
19. Language / D. Propositions / 1. Propositions
Propositions commit to content, and not to any way of spelling it out
                        Full Idea: Our talk of propositions expresses commitment to the general notion of content, without a commitment to any particular way of spelling this out.
                        From: JC Beall / G Restall (Logical Pluralism [2006], 2.1)
                        A reaction: As a fan of propositions I like this. It leaves open the question of whether the content belongs to the mind or the language. Animals entertain propositions, say I.